Reduced Density Matrix-based Valence Bond Theory

The n-body reduced density matrix (RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. A more generalized Wick’s theorem is proved, which is an extension of generalized Wick’s theorem to the case of nonorthogonal basis set and to the products of any number of reduced density operators. Using tensor analysis tool for nonorthogonal basis functions, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly expressed in terms of tensor contractions of electronic integrals and n-body RDMs of the reference VBSCF wave function. An automatic formula/code generator (AFCG) for nonorthogonal orbital-based many-electronic theory will be developed. By using AFCG, a new Hessian-based algorithm for VBSCF method is implemented. The benchmark VBSCF calculations up to 24 active electrons in 24 active orbitals are preformed.